The LSB Theorem Implies the KKM Lemma
نویسندگان
چکیده
Let S be the unit d-sphere, the set of all points of unit Euclidean distance from the origin in R . Any pair of points in S of the form x,−x is a pair of antipodes in S. Let ∆ be the d-simplex formed by the convex hull of the standard unit vectors in R. Equivalently, ∆ = {(x1, ..., xd+1) : ∑ i xi = 1, xi ≥ 0}. The following are two classical results about closed covers of these topological spaces:
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عنوان ژورنال:
- The American Mathematical Monthly
دوره 114 شماره
صفحات -
تاریخ انتشار 2007